The summary here seems to be that OP has business in Israel in the UK and finds that neither BA nor AY offer good value. There are other options which involve multiple carriers with connections in IST, FRA and so on. But, that is of course much more inconvenient and nothing avoids having to deal with TLV and a LON airport at some point in the journey.

OP simply misunderstands the nature and limitations of commercial aviation. He believes that when an aircraft is parked off-stand that the inbound pilot was lazy.

What he fails to realize and has not taken the time to understand is that the Command Captain has no say in where the aircraft is parked and that the carrier's preference is to park its aircraft at a jetbridge, but that there are more aircraft than jetbridges, thus some park offstand, necessitating the bus.

This inconvenience will continue unless one of two things happens, LHR is enlarged or the number of rotations is decreased. Will that mean fewer frequencies to/from TLV? Perhaps. But, if the service standard is that every frequency must have a jetbridge, there will be significantly fewer flights.

"Circling" the airport on arrival is a nuisance. It occurs less and less with ATC doing a better job of holding aircraft at their departure and slowing aircraft enroute so that they can be routed directly in.

But, at all major airports in the world, congestion is a fact of life. There is only so much airspace and there are more people who want to go to LON than there are cubic feet to accommodate them at some times of day. The easy solution is, of course, to limit the number of flights. But, that is unappealing to most sensible people who would suggest that imposing irreversible economic harm on the UK economy to prevent the rants of a few passengers who have not thought through their complaints is likely a poor idea.

OP's sole valid complaint is with hand luggage. It is true that BA ought to do a better job of policing that and the screaming fights which ensue can best be dealt with harshly before boarding by simply diverting those passengers to the side. But, ironically, the same sort of self-entitlement regarding hand baggage which delays flights is the sort which suggests that TLV services should have some priority for jetbridges over others.